Stockholm, Sweden (CNN) -- Authorities on Sunday were investigating whether a pair of new shootings in a southern Swedish city were connected to a single unknown gunman who is targeting immigrants living in the city.

The first shooting occurred late Saturday when someone fired a bullet into a small store in central Malmo, said police spokesman Calle Persson. The second shooting was reported around midnight, after a family alerted police to a window being shot, he said.

Both the shopkeeper and the family are immigrants living in the city. Nobody was injured in the most recent incidents.

"It is still too early to say whether this was the same gunman that we suspect for the other shootings," Persson added.

Still, the suspected serial shooter is keeping edge -- and there are no suspects.

Police say at least 15 shootings in Malmo over the last year may be linked to the one shooter, believed to be using a handgun. Sydsvenskan, a respected regional newspaper citing police sources, reported that at least five shootings can now be tied to the same weapon.

The shootings have all been well planned, under the protection of darkness and at places familiar to the shooter, according to CNN's Swedish affiliate TV4, citing police.

Several of the shootings in Malmo have occurred in recent weeks, police say. However, the first in the series is believed to be the October 2009 fatal shooting of a 20-year-old woman, said Malmo police superintendent Hans Nilsson told CNN.

"We haven't seen this kind of violence before, specifically targeting immigrants," he added.

On Thursday evening, two immigrant women were wounded when shot through their apartment window.

"I'm almost afraid of turning on the light in my apartment at night now," Shukrije Berisha, who lives in the same building, told the Swedish daily Svenska Dagbladet.

In similar incidents, two men of an "ethnic minority background" were recently shot while waiting at bus stops, according to police.

One of them "was lucky to be alive after being shot in the torso," Nilsson said.

"The shooter was most likely waiting in the bushes before firing his weapon," he said.

Basi Hassan, one of the bus stop victims, told CNN affiliate TV4 that, "I was standing here at the bus stop when I suddenly heard a shot. I don't know where it came from. Then I saw my own blood and I started feeling dizzy."

The Swedish National Murder Commission and the Swedish National Criminal Police have launched a major operation together with local police to find the gunman.

A group of psychologists is also working of trying to profile the shooter's behavior before, during and after the shootings.

Police have also increased the number of officers and K9-units patrolling the city.

In Malmo, where nearly a third of the residents are immigrants, many now fear for their safety. One 17-year-old girl, identified only as Fatima, told TV4 that she refuses to go to school by bicycle or bus and will only travel by car now.

"I couldn't sleep last night, I just couldn't stop thinking about it," she said.

The shootings also bring back memories of Sweden's "Laser-man," a shooter who was targeting immigrants in Stockholm in the 1990s with a laser-point rifle.

"We haven't had anything this big here in Sweden since the Laser-man was around," Nilsson said.

The recent slew of shootings has also prompted a mobile phone text message that has circulated among Malmo's youth. According to Nilsson, the text states: "A killer is lose in Malmo so stay indoors."

"We are very clear that we are not behind this text message, but we can also understand that people are worried," he said.

Malmo Mayor Katrin Stjernfeldt Jammeh says she is angered by the shootings.

"It is awful that people should have to be worried and feel fear for walking our streets," she said.